Description

The MODWT is used to calculate instantaneous estimates of the FD parameter,
the variance of the FD parameter and the innovations variance.
The user can select between maximum likelihood and least squares
estimators. Localized estimates may also be formed by using multiple
chi-squared degrees of freedom in estimating the FD model parameters.

Arguments

x

a vector containing a uniformly-sampled real-valued time series.

biased

a logical flag used to choose between denoting biased or unbiased
estimates. Biased estimates are those which
use all available levels in calculating
the FD model parameters. Unbiased estimates
are calculated with only those wavelet
coefficients not subject to circular filter
operations, i.e. only the interior wavelet
coefficients are used in calculating unbiased
estimates. Default: TRUE.

delta.range

a two-element vector containing the search range for the FD parameter.
Typically, the range [-10,10] is suitable for all physical systems. Default: c(-10, 10).

documentation

a character string used to describe the input
x. Default: character().

dof.order

the degree of freedom (DOF) order. The number of
chi-square DOFs used in estimating the FD
parameters is equal to 2 * dof.order + 1
where necessarily dof.order > 0. As the order
increases, the estimates will become smoother but less localized in time. Default: 0.

estimator

a character string denoting the estimation method.
Use "lse" for least squares estimates and "mle" for maximum likelihood estimates.
Default: "lse".

keep.series

a logical value. If TRUE, the original series
is preserved in the output object. Default: FALSE.

levels

a vector containing the decomposition levels. The levels may be given
in any order but must be positive. Default: 1:J where J is the maximum wavelet decomposition
level at which there exists at least one interior wavelet coefficient.

position

a list containing the arguments
from, by and to which describe the position(s) of the input
x. All position arguments need not be specified as missing members
will be filled in by their default values. Default: list(from=1, by=1, units=character()).

title.data

a character string representing the name of the input
x. Default: character().

units

a string denoting the units of the time series. Default: character() (no units).

wavelet

a character string denoting the filter type.
See wavDaubechies for details.
Default: "s8".